If a,b,c are xth,yth,zth terms of a GP respectively then (y - z) loga + (z - x) logb + (x - y) logc is?

CBSE Class 11-science Answered

If a,b,c are x^th,y^th,z^th terms of a GP respectively then (y - z) loga + (z - x) logb + (x - y) logc is?

Asked by Topperlearning User | 25 Sep, 2017, 12:01: PM

Expert Answer

$straight a equals AR to the power of straight x minus 1 end exponent straight b equals AR to the power of straight y minus 1 end exponent straight c equals AR to the power of straight z minus 1 end exponent where space straight A space and space straight R space are space first space term space and space common space ratio space respectively. loga equals logA plus left parenthesis straight x minus 1 right parenthesis logR logb equals logA plus left parenthesis straight y minus 1 right parenthesis logR logc equals logA plus left parenthesis straight z minus 1 right parenthesis logR left parenthesis straight y minus straight z right parenthesis space loga plus left parenthesis straight z minus straight x right parenthesis space logb plus left parenthesis straight x minus straight y right parenthesis space logc equals left parenthesis straight y minus straight z plus straight z minus straight x plus straight x minus straight y right parenthesis space logA space plus space left curly bracket left parenthesis straight y minus straight z right parenthesis left parenthesis straight x minus 1 right parenthesis space plus space left parenthesis straight z minus straight x right parenthesis left parenthesis straight y minus 1 right parenthesis space plus space left parenthesis straight x minus straight y right parenthesis left parenthesis straight z minus 1 right parenthesis right curly bracket space logR 0 logA plus 0 logR equals 0$

Answered by | 25 Sep, 2017, 02:01: PM